Polar Equations

r =3D ±c*cos(q) & r= =3D ±c*sin(q)<= span lang=3DEN-US style=3D'font-size:89%;mso-fareast-language:ZH-CN'>

Polar Equations<= /span>

------=_NextPart_01C816EF.740B46B0 Content-Location: file:///C:/09764A33/5PolarEquations_files/slide0178.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Polar Equations

The equations

r =3D ±c*cos(q) =

r =3D ±c*sin(q)

are circles,

tangent to the= = axes at the origin.

&nbs= p;

r =3D ±c*cos(q) & r= =3D ±c*sin(q)<= span lang=3DEN-US style=3D'font-size:89%;mso-fareast-language:ZH-CN'>

Polar Equations<= /span>

------=_NextPart_01C816EF.740B46B0 Content-Location: file:///C:/09764A33/5PolarEquations_files/slide0177.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Polar Equations

The equations

r =3D ±c*cos(q) =

r =3D ±c*sin(q)

are circles,

tangent to the= = axes at the origin.

&nbs= p;

r =3D ±c*cos(q) & r= =3D ±c*sin(q)<= span lang=3DEN-US style=3D'font-size:89%;mso-fareast-language:ZH-CN'>

Example A: Graph r =3D -sin(q)

r = ; q

0 = ; 0

-½ = ; &= #960;/6

-Ö<= /span>2/2 π/4

-Ö<= /span>3/2 π/3

-1 = ; &= #960;/2

-Ö<= /span>3/2 2π/3

-Ö<= /span>2/2 3π/4

-½ 5π/6

0 = ; &= #960;

Ó F= = r= a= n= k= M= a = 2= 0= 0= 6

Polar Equations<= /span>

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&nbs= p;

r =3D ±c*cos(q) & r= =3D ±c*sin(q)<= span lang=3DEN-US style=3D'font-size:89%;mso-fareast-language:ZH-CN'>

Example A: Graph r =3D -sin(q)

r = ; q

0 = ; 0

-½ = ; &= #960;/6

-Ö<= /span>2/2 π/4

-Ö<= /span>3/2 π/3

-1 = ; &= #960;/2

-Ö<= /span>3/2 2π/3

-Ö<= /span>2/2 3π/4

-½ 5π/6

0 = ; &= #960;

Ó F= = r= a= n= k= M= a = 2= 0= 0= 6

Polar Equations<= /span>

r = ; q = ;

0 = ; π

½ = ; 7π/6

Ö2/2 5<= span lang=3DEL style=3D'font-family:"Times New Roman";mso-ascii-font-family:Ari= al; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:Arial;font-si= ze: 133%;color:#006600;mso-fareast-language:ZH-CN'>π/4

Ö3/2 4<= span lang=3DEL style=3D'font-family:"Times New Roman";mso-ascii-font-family:Ari= al; mso-bidi-font-family:"Times New Roman";mso-hansi-font-family:Arial;font-si= ze: 133%;color:#006600;mso-fareast-language:ZH-CN'>π/3

1 = ; 3π/2

Ö3/2 5π/3

Ö2/2 7π/4

½ 11π/60 = ; 2π

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&nbs= p;

r =3D ±c*cos(q) & r= =3D ±c*sin(q)<= span lang=3DEN-US style=3D'font-size:89%;mso-fareast-language:ZH-CN'>

r = ; q

0 = ; 0

-½ = ; &= #960;/6

-Ö<= /span>2/2 π/4

-Ö<= /span>3/2 π/3

-1 = ; &= #960;/2

-Ö<= /span>3/2 2π/3

-Ö<= /span>2/2 3π/4

-½ 5π/6

0 = ; &= #960;

Ó F= = r= a= n= k= M= a = 2= 0= 0= 6

Polar Equations<= /span>

r = ; q = ;

0 = ; π

½ = ; 7π/6

1 = ; 3π/2

Ö3/2 5π/3

Ö2/2 7π/4

½ 11π/60 = ; 2π

Example A: Graph r =3D -sin(q)

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r =3D c(1= ± cos(q)) & r =3Dc(1 &plu= smn; sin(q))

Example B: Graph r =3D 1 – sin(q)

r = ; q

1 = ; π

3/2 = ; 7π/6

= 1+Ö2/2 5= π= /4

= 1+Ö3/2 4= π= /3

= 2 = ; 3π/2

= 1+Ö3/2 5= π= /3

= 1+Ö2/2 7= π= /4

3/2 11π/6

= 1 = ; 2π

r = ; q= 3;

1 = ; 0

½ = ; π/6

1-Ö2/2 π/4

1-Ö3/2 π/3

0 = ; π/2

1-Ö3/2 2π/3

1-Ö2/2 3π/4

½ = ; 5π/6

1 = ; π

Polar Equations<= /span>

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&nbs= p;

r = ; q

1 = ; π

3/2 = ; 7π/6

= 1+Ö2/2 5= π= /4

= 1+Ö3/2 4= π= /3

= 2 = ; 3π/2

= 1+Ö3/2 5= π= /3

= 1+Ö2/2 7= π= /4

3/2 11π/6

= 1 = ; 2π

r = ; q= 3;

1 = ; 0

½ = ; π/6

1-Ö2/2 π/4

1-Ö3/2 π/3

0 = ; π/2

1-Ö3/2 2π/3

1-Ö2/2 3π/4

½ = ; 5π/6

1 = ; π

Polar Equations<= /span>

r =3D c(1= ± cos(q)) & r =3Dc(1 &plu= smn; sin(q))

Example B: Graph r =3D 1 – sin(q)

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file:///C:/09764A33/5PolarEquations_files/slide0058.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Polar Equations

&nbs= p;

r = ; q

1 = ; π

3/2 = ; 7π/6